The square of an imaginary number is an imaginary number or a negative real number. In mathematics, a number with an even exponent whose power is a negative number is defined as a pure imaginary number. All imaginary numbers are complex numbers. It is defined as i=-1. But imaginary numbers have no arithmetic roots, so ±√(-1)=±i. For z=a+bi, it can also be expressed as e raised to the power of iA, where e is a constant, i is the imaginary unit, and A is the argument of the imaginary number, which can be expressed as z=cosA+isinA.
A pair of real numbers and imaginary numbers is regarded as one number in the range of complex numbers and is named a complex number. Imaginary numbers are neither positive nor negative. Complex numbers that are not real numbers, even purely imaginary numbers, cannot be compared.
The square of an imaginary number is an imaginary number or a negative real number. In mathematics, a number with an even exponent whose power is a negative number is defined as a pure imaginary number. All imaginary numbers are complex numbers. It is defined as i=-1. But imaginary numbers have no arithmetic roots, so ±√(-1)=±i. For z=a+bi, it can also be expressed as e raised to the power of iA, where e is a constant, i is the imaginary unit, and A is the argument of the imaginary number, which can be expressed as z=cosA+isinA.
The origin of imaginary numbers
With the development of mathematics, mathematicians have discovered that the real roots of some cubic equations must be expressed by the square roots of negative numbers. Moreover, if the square roots of negative numbers are admitted, then the problem of whether algebraic equations have roots can be solved, and a satisfactory result will be obtained that n-degree equations have n roots. In addition, the square root of a negative number is calculated according to the arithmetic rules of numbers, and the result is also correct.
The Italian mathematician Cardin made a compromise. He called the square root of a negative number a "fictitious number", which means that it can be recognized as a number, but it cannot represent an actual quantity like a real number. is fictional. By 1632, the French mathematician Descartes officially gave the square root of a negative number a name that everyone was happy to accept - imaginary number.
The imaginary word for an imaginary number means that it does not represent an actual number, but only exists in imagination. Although imaginary numbers are "imaginary", mathematicians have not relaxed their research on them. They have discovered many properties and applications of imaginary numbers. The great mathematician Euler proposed the concept of "imaginary unit". He regarded U as the imaginary unit, represented by the symbol i, which is equivalent to the real unit 1. When imaginary numbers have units, they can be written as multiples of the imaginary units just like real numbers.
Since then, mathematicians have treated real numbers and imaginary numbers equally and called them complex numbers. As a result, the number family has been unified. Any complex number can be written in the form of a+bi. When b=0, a+bi=a, it is a real number. When b#0, a+bi is an imaginary number.